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Answer:
First of all, let us have a look at the formula for Total Surface Area of triangular prism:
TSA = B + p\times hTSA=B+p×h
Where B is the area of base
p is the perimeter of base and
h is the height of prism.
here base is a right angled triangle (because 3, 4, 5 is a triplet) Base and Height will be 3 , 4 cm or 4, 3 cm and 5 will be hypotenuse.
So formula for B:
\begin{gathered}B = \dfrac{1}{2}\times Base \times Height\\B = \dfrac{1}{2}\times 3\times 4 = 6 cm^2\end{gathered}
B=
2
1
×Base×Height
B=
2
1
×3×4=6cm
2
So, TSA = 6 + (3+4+5) \times× 10 = 6 + 120 = 126 cm^2cm
2
So, total surface area of given prism is 126cm^2cm
2
.